Integrability of the sums of the trigonometric series 1/2 aₒ + ∞ [over] Σ [over] n=1 a_n cos nΘ and ∞ [over] Σ [over] n=1 a_n sin nΘ

Alternative Title

Integrability of the sums of the trigonometric series the cosine series and the sine series

Author

John William Garrett

Abstract

"The trigonometric series C = 1/2 aₒ + ∞ [over] Σ [over] [n=1] a[subscript n] cos nΘ and S = ∞ [over] Σ [over] n=1 a[subscript n] sin nΘ, where {a[subscript n]} monotonically decreases to zero both converge almost everywhere to functions f and g respectively. f (or g) is L iff C (or S) is the Fourier series of f (or g) iff term-by-term integration of C (or S) is valid. There are three equivalent conditions, each of which implies that C is the Fourier series of f...."--Abstract, page ii.

Advisor(s)

Stanojević, Časlav V., 1928-2008

Committee Member(s)

Plummer, O. R.
Dekock, Arlan R.

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1971

Pagination

vi, 39 pages

Rights

© 1971 John William Garrett, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Subject Headings

Fourier series
Integral equations

Thesis Number

T 2539

Print OCLC #

6036921

Electronic OCLC #

871705843

Link to Catalog Record

http://merlin.lib.umsystem.edu/record=b1066460~S5

Recommended Citation

Garrett, John William, "Integrability of the sums of the trigonometric series 1/2 aₒ + ∞ [over] Σ [over] n=1 a_n cos nΘ and ∞ [over] Σ [over] n=1 a_n sin nΘ" (1971). Masters Theses. 7212.
https://scholarsmine.mst.edu/masters_theses/7212